Various types of rotary engines and pumps have been devised in the past which utilize the turning motion of a series of vanes within compression chambers to generate power. Representative of such approaches is the rotary piston pump disclosed in U.S. Pat. No. 3,895,893 to M. Sommer wherein generally disk-shaped vanes are mounted on shafts to undergo movement through an annular chamber having a pumping area of generally circular cross-section. The vanes are free to turn about radial axes perpendicular to their direction of movement while advancing through one portion of the chamber and also can turn approximately 90.degree. to advance through another portion of the chamber. U.S. Pat. No. 4,599,976 to P. V. Meuret typifies another approach in which a rotary piston is in the shape of a semi-circular vane on a rotating shaft. Similar approaches are disclosed in other U.S. Pat. No. including U.S. Pat. No. 2,816,527 to Q. Palazzo, No. 3,871,337 to E. H. Green et al and No. 3,594,104 to J. Speese. None, however, utilizes the rotational movement of a lever arm about a center axis to cause turning or rotational movement of a vane-type piston about another lever arm and in such a way as to rotate the piston through a compression chamber to compress a gas as a preliminary to ignition or firing; further wherein the firing in each chamber will impart translational movement to the associated vane-type piston and consequent turning or rotational movement of the vane-type piston on or about the first lever arm; and additionally to so arrange a series of vanetype pistons with respect to one or more compression chambers as to establish a multi-stroke engine capable of performing useful work in a dependable and efficient manner.